ie one side foil shaped. the other side flat. Like outer fins on a surfboard?

Trying different thinks out on my mutant. That is one of the things I want to try.

I want to see what the difference is on the wave face.

Big difference.
After 30yrs on smaller waveboards, somebody has finally tried it for sidefins on windsurf boards (quads and thrusters) and the results are worth investigating.
Google K4 Fins "ezzy assymetrical" and see if applicable to what u r doing Plummet.

Also consider toe-in as the water is not running straight along the longitudinal axis of your board. It doesn't on a surf / windsurf board so I doubt it does on your twinny, and toe in can be quite effective in reducing drag and increasing wave performance. Given the edging it will be a bit different but there can be great effect realised in experimenting with such things.

We built some asymmetric fins, some 70/30 some more like 90/10. We tried them facing in, facing out and compared them to std 50/50 fins. Could not find any noticeable difference.
The fins on a TT just provide tracking and in my opinion the depth, area and durability are the main points to play with

On my Shinn Wave "mutant" I ride with a tri fin set up at the back. The right-side fin (which is in the water toe side since I'm a natural footer) is as large as the centre fin (both about 120mm deep) and the left side fin is 50mm deep (heel side when riding normally). The two fins at the front are smaller again (40mm which is all you need when riding the thing tail first).

This configuration gives me more bite in the forehand bottom turns and for carving a deep forehand turn on flat water.

^^ Would have to agree with Adrian here. The Shinn lacks decent surfboard style rails midship. This would improve the wave riding considerably.

Cheers that's interesting advice.

I'll think about doing a wrapped rail for my next board. Its getting pretty technical for bloke building his own boards in his garage with hand tools.